ERGODIC AND FIXED POINT THEOREMS FOR BREGMAN NONEXPANSIVE SEQUENCES AND MAPPINGS IN BANACH SPACES

被引：0

作者：

Rouhani B.D. ^{[1
]}

Khatibzadeh H. ^{[2
]}

Mohebbi V. ^{[1
]}

机构：

[1] Department of Mathematical Sciences, University of Texas at El Paso, El Paso, 79968, TX

[2] Department of Mathematics, University of Zanjan, Zanjan

来源：

Applied Set-Valued Analysis and Optimization | 2022年 / 4卷 / 03期

关键词：

Asymptotic behavior; Asymptotically regular sequence; Bregman nonexpansive sequence; Strong convergence; Weak convergence;

D O I：

10.23952/asvao.4.2022.3.05

中图分类号：

学科分类号：

摘要：

In this paper, we introduce the notion of Bregman nonexpansive sequences and mappings in a Banach space, prove an ergodic theorem and a fixed point theorem, and some weak convergence theorems for such sequences and maps with rather mild assumptions on the Banach space. These results extend our previous results for φ-nonexpansive sequences and give a partial answer to the open problem raised in 1981 by Djafari Rouhani for nonexpansive sequences in a Banach space. ©2022 Applied Set-Valued Analysis and Optimization.

引用

页码：311 / 321

页数：10

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